Integral of x+(1/x) dx

The solution

You have entered [src]

  1           
  /           
 |            
 |  /    1\   
 |  |x + -| dx
 |  \    x/   
 |            
/             
0

$$\int\limits_{0}^{1} \left(x + \frac{1}{x}\right)\, dx$$

Integral(x + 1/x, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
1. The integral of $\frac{1}{x}$ is $\log{\left(x \right)}$ .
The result is: $\frac{x^{2}}{2} + \log{\left(x \right)}$
Add the constant of integration:

$\frac{x^{2}}{2} + \log{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{x^{2}}{2} + \log{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                   2         
 | /    1\          x          
 | |x + -| dx = C + -- + log(x)
 | \    x/          2          
 |                             
/

$$\int \left(x + \frac{1}{x}\right)\, dx = C + \frac{x^{2}}{2} + \log{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

44.5904461339929

44.5904461339929

The graph

Use the examples entering the upper and lower limits of integration.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of x+(1/x) dx

Limits of integration:

The graph:

Piecewise:

The solution